How to render HTML content using the Interactivity API?

Rather than binding text with a directive, you could bind a callback with data-wp-watch that sets the inner HTML of the div when it runs:

<div data-wp-watch="callbacks.renderContent"></div>

callbacks: {
    renderContent() {
        const context = getContext();
        const element = getElement();

        element.ref.innerHTML = context.randomPost.content.rendered;
    },
},

Since the callback uses context.randomPost.content.rendered, it should run any time that value changes.